The ailing leader, who has been in power since 1999, had already abandoned plans to seek a fifth term as opposition to his authority increased.
The Algerian army had called for Mr Bouteflika, 82, to be declared incapable of carrying out his duties.
The former president suffered a serious stroke in 2013 and has made very few public appearances.
His resignation was announced with a statement which was aired by state news agency APS.
The statement read: “The president of the republic, Abdelaziz Bouteflika, has officially notified the president of the constitutional council of his decision to end his mandate as president of the republic”.
APS reported that the resignation would come into effect immediately.
When did it all start?
Mass protests which began in Algiers gradually spread across the country throughout February, when Mr Bouteflika’s announced his intention to stand for a fifth term.
Tens of thousands peacefully demonstrated and on Friday 1 March Mr Bouteflika vowed not to serve out a fifth term if re-elected.
However, with that promise along with a change of prime minister, protesters remained unsatisfied.
Prominent figures who have been leading the protests also rejected Mr Bouteflika’s offer this week that he would leave by the end of his current term on Sunday 28 April.
It appears the powerful military agreed.